When posing a rigged mesh I get really weird results
Go into weight paint mode on the object and select your "hand.L" vertex group. You'll see that the vertex group for hand.L is partially assigned on the geometry of the lower left arm. Remove that area from your vertex group. In the image below, that red on the lower arm before the wrist shouldn't be there for the hand.L group.


https://docs.blender.org/manual/en/latest/sculpt_paint/weight_paint/introduction.html



See how I have the upperArm.l group selected and lowerArm.l part of the mesh is light blue, that means weight for the upper arm is still assigned to the mesh for the lower arm.



Select the verts for lower arm and hand, with the upperArm.l group select, assign a weight of 0 to those verts for the upperArm.l group. That fixes the issue.